If a^2-5a+1 =0 Then find a^2+(1/a)^2
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Answer:
23
Step-by-step explanation:
a² - 5a + 1 = 0
Transposing 5a to RHS
⇒ a² + 1 = 5a
Transposing a to LHS
⇒ ( a² + 1 ) / a = 5
⇒ a²/a + 1/a = 5
⇒ a + 1/a = 5
Squaring on both sides
⇒ ( a + 1/a )² = 5²
Since ( x + y )² = x² + y² + 2xy
⇒ a² + 1/a² +2( a )( 1/a ) = 25
⇒ a² + 1/a² + 2 = 25
Transposing 2 to RHS
⇒ a² + 1/a² = 25 - 2
⇒ a² + 1/a² = 23
Hence the value of a² +1/a² is 23.
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